Here are reported the results obtained during the measurements for the different fibers of the ITU Round Robin.
In table A.2 and A.3 are shown the characteristics of the fiber as reported by the ITU Round Robin organizer (Prof. Y. Namihira) together with the average values obtained in Geneva for the n2/Ae f f and for the n2with relative errors. In this case the absolute maximum deviation (MD) from the average is used as an estimate for the error (two measurements were taken).
In the other following tables, in each one are reported in more details the values obtained for all the fibers.
In table A.4 and A.5 are shown the values obtained during each measurement for all the fibers. Are given the splice loss β, the total attenuation along the fiber β0, the Faraday Mirror lossβ00, the efficient length L∗e f f, the n2/Ae f f and relative error, the n2
and relative error, and the χ2. The errors on n2/Ae f f are the one obtained from the fit of the data.
In table A.6 and A.7 are reported the same results but on other measurements taken on a different day.
Final Data for the Fibers L-1 .. L-4
Fiber ID Fiber 1-L Fiber 2-L Fiber 3-L Fiber 4-L (SMF, G.652) (CSF, G.654) (DSF1, G.653) (DSF2, G.653)
L (km) 5.36 7.65 4.43 4.82
α(dB/km) 0.19 0.17 0.21 0.21
@1550 nm
D (ps/nm/km) +16.0 +19.0 -0.63 -1.30
@1550 nm
Ae f f (µm2) 84.5 88.2 46.7 45.6
@1550 nm
n2/Aeff(VALUE) 3.16 3.2 5.6 5.9
(10−10W−1)
n2/Ae f f (MD) 0.06 0.1 0.1 0.3
(10−10W−1)
n2(VALUE) 2.67 2.8 2.64 2.7
(10−20m2W−1)
n2(MD) 0.07 0.1 0.09 0.2
(10−20m2W−1)
Table A.2: Parameters and final values for the n2/Ae f fof the first set of fibers. ITU Round Robin. The absolute maximum deviation from the average is used as an estimate for the error.
Final Data for the Fibers L-5 .. L-8
Fiber ID Fiber 5-L Fiber 6-L Fiber 7-L Fiber 8-L
(NZDSF1,G.655) (NZDSF2,G.655) (NZDSF3,G.655) (DSC)
L (km) 6.96 4.4 5.46 2.95
α(dB/km) 0.20 0.20 0.20 0.50
@1550 nm
D (ps/nm/km) -2.27 +4.63 -2.52 -108.4
@1550 nm
Ae f f (µm2) 55.5 51.3 72.7 22.8
@1550 nm
n2/Aeff(VALUE) 5.23 5.8 4.0 17.5
(10−10W−1)
n2/Ae f f (MD) 0.07 0.1 0.1 0.4
(10−10W−1)
n2(VALUE) 2.91 2.97 2.9 3.9
(10−20m2W−1)
n2(MD) 0.07 0.09 0.1 0.2
(10−20m2W−1)
Table A.3: Parameters and final values for the n2/Ae f f of the second set of fibers. ITU Round Robin.
The absolute maximum deviation from the average is used as an estimate for the error.
First Measurement on Fibers L-1 .. L-4
Fiber ID Fiber 1-L Fiber 2-L Fiber 3-L Fiber 4-L (SMF, G.652) (CSF, G.654) (DSF1, G.653) (DSF2, G.653)
Splice Lossβ 0.1 .15 0.3 0.3
(dB)
Total Attenuationβ0 0.9 1.75 1.15 1.6
(dB)
FM Lossβ00 1.77 1.77 1.77 1.77
(dB)
Le f f 7.27 8.79 5.33 6.01
(km)
n2/Aeff (VALUE) 3.10 3.30 5.53 5.58
(10−10W−1)
n2/Ae f f (FIT ERROR) 0.02 0.05 0.02 0.02
(10−10W−1)
n2(VALUE) 2.62 2.91 2.58 2.54
(10−20m2W−1)
n2(FIT ERROR) 0.03 0.06 0.04 0.04
(10−20m2W−1)
χ2 0.0001 0.003 0.00001 0.0001
Table A.4: Experimental values for the first measurement on the first set of fibers. ITU Round Robin.
Errors are from the fit.
First Measurement on Fibers L-5 .. L-8
Fiber ID Fiber 5-L Fiber 6-L Fiber 7-L Fiber 8-L
(NZDSF1,G.655) (NZDSF2,G.655) (NZDSF3,G.655) (DCF)
Splice Lossβ 0.2 0.3 0.1 1.7
(dB)
Total Attenuationβ0 1.4 0.7 1.3 1.9
(dB)
FM Lossβ00 1.77 1.77 1.77 1.77
(dB)
Le f f 8.24 5.72 6.94 1.91
(km)
n2/Aeff (VALUE) 5.16 5.67 3.85 17.8
(10−10W−1)
n2/Ae f f (FIT ERROR) 0.03 0.02 0.02 0.1
(10−10W−1)
n2(VALUE) 2.86 2.91 2.80 4.1
(10−20m2W−1)
n2(FIT ERROR) 0.04 0.04 0.03 0.1
(10−20m2W−1)
χ2 0.0003 0.0001 0.0001 0.0001
Table A.5: Experimental values for the first measurement on the second set of fibers. ITU Round Robin. Errors are from the fit.
Second Measurement on Fibers L-1 .. L-4
Fiber ID Fiber 1-L Fiber 2-L Fiber 3-L Fiber 4-L (SMF, G.652) (CSF, G.654) (DSF1, G.653) (DSF2, G.653)
Splice Lossβ 0.2 0.1 0.3 0.4
(dB)
Total Attenuationβ0 0.8 1.3 1.0 0.9
(dB)
FM Lossβ00 1.77 1.77 1.77 1.77
(dB)
Le f f 7.42 9.61 5.57 6.07
(km)
n2/Aeff (VALUE) 3.23 3.18 5.78 6.23
(10−10W−1)
n2/Ae f f (FIT ERROR) 0.02 0.02 0.02 0.02
(10−10W−1)
n2(VALUE) 2.73 2.80 2.70 2.84
(10−20m2W−1)
n2(FIT ERROR) 0.03 0.03 0.04 0.04
(10−20m2W−1)
χ2 0.0005 0.003 0.001 0.0006
Table A.6: Experimental values for the second measurement on the first set of fibers. ITU Round Robin. Errors are from the fit.
Second Measurement on Fibers L-5 .. L-8
Fiber ID Fiber 5-L Fiber 6-L Fiber 7-L Fiber 8-L
(NZDSF1,G.655) (NZDSF2,G.655) (NZDSF3,G.655) (DCF)
Splice Lossβ 0.1 0.2 0.2 1.4
(dB)
Total Attenuationβ0 1.4 1.0 1.1 1.5
(dB)
FM Lossβ00 1.77 1.77 1.77 1.77
(dB)
Le f f 8.60 5.60 6.88 2.23
(km)
n2/Aeff (VALUE) 5.31 5.89 4.08 17.3
(10−10W−1)
n2/Ae f f (FIT ERROR) 0.02 0.02 0.02 0.4
(10−10W−1)
n2(VALUE) 2.95 3.02 2.97 3.8
(10−20m2W−1)
n2(FIT ERROR) 0.04 0.04 0.03 0.2
(10−20m2W−1)
χ2 0.0003 0.0001 0.0001 0.0001
Table A.7: Experimental values for the second measurement on the second set of fibers. ITU Round Robin. Errors are from the fit.
Channel Bit Rate Capacity Distance NBL Product N B (Gbps) NB (Gbps) L (km) (Tbps·km)
10 10 100 50 5
Published Articles
1. Measurement of nonlinear polarization rotation in high birefringence optical fibers at telecom wavelength.
C. Vinegoni, M. Wegmuller, B. Huttner, and N. Gisin J. Opt. A: Pure Appl. Opt., Vol. 2 (2000) pp. 314-18
2. All optical switching in a highly birefringent and a standard telecom fiber using a Faraday mirror stabilization scheme.
C. Vinegoni, M. Wegmuller, B. Huttner, and N. Gisin Opt. Comm., Vol. 182 (2000) pp. 314-18
3. Determination of the nonlinear coefficient n2/Ae f f using a self-aligned interfer-ometer and a Faraday mirror.
C. Vinegoni, M. Wegmuller, N. Gisin
Electronic Letters, Vol. 36 (2000) pp. 886-87
4. Measurements of the nonlinear coefficient of standard SMF, DSF, and DSC fibers using a self-aligned interferometer and a Faraday mirror.
C. Vinegoni, M. Wegmuller, and N. Gisin
Photonics and Technology Lett., December 2001
5. Distributed gain measurements in Er-doped fibers with high resolution and ac-curacy using an Optical Frequency Domain Reflectometer
M. Wegmuller, P. Oberson, O. Guinnard, B.Huttner, L. Guinnard, C. Vinegoni, N.
Gisin
J. Lightwave Technol., Vol. 18 (2000) pp. 2127-32
6. Analysis of the polarization evolution in a ribbon cable using high resolution OFDR
M. Wegmuller, M. Legre, P. Oberson, O. Guinnard, L. Guinnard, C. Vinegoni, N.
Gisin
Photonics and Technology Letters, Vol.. 13 (2000) pp. 145-7
137
7. A near field scanning optical microscope in single photon detection mode at 1.55 µm.
C. Vinegoni, H. Deriedmatten, M. Wegmuller, N. Gisin, Y. Mugnier, A. Jalocha, P.
Descouts Submitted
8. Determination of polarization coupling length in telecom fibers exploiting non-linear polarization rotation.
C. Vinegoni, V. Scarani, M. Wegmuller, and N. Gisin Submitted
9. Emulator of first and second order polarization mode dispersion.
M. Wegmuller, S. Demma, C. Vinegoni, and N. Gisin Photonics and Technology Lett. , Vol. 14 (2002) pp. 630-2
10. Distributed measurements of chromatic dispersion and nonlinear coefficient in low PMD dispersion shifted fibers.
C. Vinegoni, H. Chen, M. Leblanc, G. Schinn, M. Wegmuller, and N. Gisin Submitted
B.1 Measurement of nonlinear polarization rotation in high birefringence optical fibers at telecom
wavelength.
C. Vinegoni, M. Wegmuller, B. Huttner, and N. Gisin
1 Group of Applied Physics - Gap Optique University of Geneva,
20 Ecole-de-Medecine, CH-1211 Aeneve 4, Switzerland Claudio.Vinegoni@physics.unige.ch
Abstract : We present both a theoretical and experimental analysis of nonlinear polarization rotation in an optical fiber. Starting from the coupled non-linear Schr ¨odinger equations an an-alytical solution for the evolution of the state of polarization, valid for fibers with large linear birefringence and quasi cw input light with arbitrary polarization, is given. It allows to model straightforwardly go-and-return paths as in interferometers with standard or Faraday mirrors.
In the experiment all the fluctuations in the linear birefringence, including temperature and pressure induced ones, are successfully removed in a passive way by using a double pass of the fiber under test with a Faraday mirror at the end of the fiber. This allows us to use long fibers and relatively low input powers. The match between the experimental data and our model is excellent, except at higher intensities where deviations due to modulation instability start to appear.
PUBLISHED : J. Opt. A: Pure Appl. Opt., Vol. 2 (2000) pp. 314-18
Measurement of nonlinear
polarization rotation in a highly birefringent optical fibre using a Faraday mirror
C Vinegoni, M Wegmuller, B Huttner and N Gisin
Group of Applied Physics, University of Geneva, 20 Ecole-de-Medecine, CH-1211 Geneve 4, Switzerland
E-mail:claudio.vinegoni@physics.unige.ch Received 14 December 1999, in final form 30 March 2000
Abstract.We present both a theoretical and experimental analysis of nonlinear polarization rotation in an optical fibre. Starting from the coupled nonlinear Schr¨odinger equations an analytical solution for the evolution of the state of polarization, valid for fibres with large linear birefringence and quasi cw input light with arbitrary polarization, is given. It allows us to model straightforwardly go-and-return paths as in interferometers with standard or Faraday mirrors. In the experiment all the fluctuations in the linear birefringence, including temperature- and pressure-induced ones, are successfully removed in a passive way by using a double pass of the fibre under test with a Faraday mirror at the end of the fibre. This allows us to use long fibres and relatively low input powers. The match between the experimental data and our model is excellent, except at higher intensities where deviations due to modulation instability start to appear.
Keywords:Nonlinear polarization rotation, nonlinear birefringence, Keff effect, Faraday mirror
1. Introduction
The potential of nonlinear polarization rotation (NPR) to build ultrafast devices was recognized a long time ago and has received considerable attention since then. It has been proposed to exploit it for optical switches [1], logic gates [2], multiplexers [3], intensity discriminators [4], nonlinear filters [5], or pulse shapers [6]. However, an inherent problem with all these applications is the stability of the output state of polarization, generally subjected to fluctuations of the linear birefringence caused by temperature changes and drafts in the fibre environment. Of course, the same problem was also encountered in the few experiments dealing with the characterization and measurement of the NPR itself. In [7], the fluctuations of the output polarization were too strong to allow a meaningful measurement of NPR in a polarization maintaining fibre at 1064 nm, and in [8], where 514 nm light was injected into a 60 m long fibre with a beat length of 1.6 cm, a complicated arrangement had to be employed for the extraction of the changes caused by temperature drifts.
As the fluctuations become worse for fibres with a large birefringence, and as the effect of NPR is proportional to the inverse of the wavelength, it is hard to measure NPR directly in a polarization-maintaining (PM) fibre at the telecom wavelength of 1.55µm. In this work we propose a method for removing the overall linear birefringence, and therefore
also its fluctuations, in a passive way by employing a Farady mirror (FM) [9] and a double pass of the fibre under test.
To check how this—nowadays standard—method [10–13] of removing linear birefringence acts on the NPR, we develop in section 2 of this paper a simple model to calculate the action of linear and nonlinear birefringence. Using this model, it is then easy to show that the proposed method removes the overall linear birefringence only, whereas the nonlinear one, leading to NPR, remains unchanged. After describing the experimental setup, the results of our NPR measurements using a FM are presented in section 3, along with the predictions from our analytical model. The excellent agreement between the two demonstrates that using the FM, the overall linear birefringence is indeed removed completely, allowing one to observe the NPR otherwise hidden within the noisy background of polarization changes due to environmental perturbations. This result also validates our method for possible implementation with a variety of other applications like the ones mentioned at the beginning of this section, with the prospect of drastically increasing their polarization stability.
2. Theoretical background
In a dielectric medium, an intense elliptical input pulse induces birefringence—via the optical Kerr effect—due to 1464-4258/00/040314+05$30.00 © 2000 IOP Publishing Ltd
Figure 1.Evolution of the state of polarization as represented on the Poincar´e sphere. (a) Polarization ellipse self-rotation in an isotropic medium. The Stokes vector is rotating around theσ3axis with an angle proportional to the length of the medium, the input intensity, and the sine of the input ellipticity.
(b) High-birefringence fibre. The rotation of the Stokes vector mainly consists of a fast rotation around the axis of linear birefringenceσθ, whereas the slow rotations due to the nonlinear birefringence can be considered as small perturbations.
the different amounts of intensity along the major and minor axis of the polarization ellipse. It is well known that in isotropic media this self-induced birefringence leads to a rotation of the polarization ellipse while propagating in the medium [14, 15] (the effect is consequently often called polarization ellipse self-rotation and its representation on the Poincar´e sphere is shown in figure 1(a)). In fact, measuring this ellipse rotation is one of the standard ways to evaluate the cubic optic nonlinearity of the medium [16]. In an optical fibre however, the situation becomes more complicated as there is also the local intrinsic birefringence to be considered.
Generally, the polarization ellipse changes are hard to predict in that case as the linear and nonlinear birefringence interact in a complicated manner.
To formulate this more precisely, we start with the coupled nonlinear Schr¨odinger equations describing the propagation of light in an optical fibre. For cw input light, time derivatives drop out, and we can write the equation in a similar form as Menyuk [17] when assuming a lossless, linearly birefringent fibre and by neglecting polarization mode coupling:
∂zψ= −i(ωBσθ+ωασ3ψσ3)ψ. (1)
E1(z)andE2(z)at the positionzalong the fibre. The first term in the right-hand side describes the linear birefringence, whereω is the optical frequency andB the birefringence (in s m−1). Note thatB is assumed to be independent of ω, an excellent approximation for standard fibres. The phase birefringenceωBis multiplied byσθ=σ1cos(θ)+σ2sin(θ), corresponding to linear birefringence in theθdirection, with σ1,2,3 being the 2×2 Pauli matrices. The second term in the right-hand side of (1) accounts for the nonlinear birefringence, withα=3ncA2Peff, andσ3ψz=|E|E1|2−|E2|2
1|2+|E2|2.Pis the total light power,n2the nonlinear refractive index,Aeff
the effective mode area, andcthe speed of light.
For an intuitive understanding of the action of the two terms in the right-hand side of (1), it is better to revert to the Stokes formalism. On the Poincar´e sphere, the first term describes a rotation of the polarization vector (Stokes vector) around axis σθ, lying on the equator and corresponding to linear birefringence. Similarly, the second term is a rotation around the vertical axis corresponding to nonlinear birefringence. However, equation (1) shows that the speed and the rotation direction in this case depends on the polarization state throughσ3ψ, as is illustrated in figure 1(b). Consequently, the two rotations are linked in a complicated manner, and the resulting evolution of the polarization vector is not obvious.
Fortunately, in standard telecom fibres, the speed of rotation around the vertical axis is much smaller than the one around the birefringent axis σθ even at considerable power levels. This is because in such fibres B α (see (1)). For example, a fibre with a beat length of 10 m hasB≈0.5 ps km−1whileα≈0.006 ps km−1for a power of 10 W (λ=1550 nm,n2=3.2×10−20,Aeff=60µm2) (note that in this work, a PM fibre will be used with a beat length in the mm range, making the ratioBα as large as 107).
The slow rotation due to the nonlinear birefringence can therefore be treated as a perturbation that merely changes the angular frequency of the fast rotation caused by the linear birefringence. This becomes more obvious by rewriting (1) as
∂zψ= −iωBσθψ−iωα12(σ3ψσ3
+(1− σθ+π2ψσθ+π2− σθψσθ))ψ (2) where the identityψ = σψσψ, valid for allψ, has been used. The term proportional to ψ affects only the global phase and can be neglected. Further, the two termsσ3ψσ3
andσθ+π2ψσθ+π2 cancel each other to first order—this can be intuitively understood from figure 1(b) and was confirmed by numerical simulations—producing only a small (second-order) precession of the instantaneous rotation axis. Hence we obtain the following approximation for the evolution of the polarization vector:
norm|ψ|2reflecting that we did not take into account losses.
Note further that when applying (3) for linearly polarized input light we obtain the same formula as in [4].
The solution of (3) is straightforward, ψz = exp(−iωBeffσθz)ψ0, and corresponds to a rotation of the input polarization vector around the linear birefringence axis σθ, with a rotation angleβgiven by
β=ω B−α
2mθ(0)
z. (5)
mθ(0)is the projection of the input polarization vector on the birefringence axisσθ, andzthe distance from the input end.
In principle, the NPR, caused by the nonlinear response of the single-mode fibre to the input state, could now be measured by varying the input power and observing the corresponding change in the output polarization vector.
However, from a practical standpoint, this will be hardly possible as equation (5) shows that slightest changes in the linear birefringenceBwill completely cover the nonlinear, intensity-dependent ones (remember that B α for reasonable input power levels). Indeed, earlier work [8, 18]
greatly suffered from temperature- and pressure-induced changes ofB always present in a laboratory environment, even though they were using short fibres.
Nowadays, a simple and efficient way to get rid of any kind of fluctuation in the intrinsic birefringence is to make a double pass of the fibre under test by means of a FM [9, 10].
The linear birefringence accumulated during the forward path is then automatically compensated on the return path.
However, it is nota prioriclear what will happen to the nonlinear birefringence.
To investigate this point, we rewrite the solution of (3) in the Stokes formalism,
m(L)= ˆRθ(β(L))m(0) (6) wherem(0)is the input Stokes vector, Rˆθ is a rotation operator around the axisσθ, andβis as given by (5). Applying the action of the FM,mF(L)= −m(L)(the superscriptF indicates the state of polarization after reflection from the FM), and of the return path,Rˆ−θ1, we get
The result shows that the rotation due to the nonlinear birefringence of the forward and return path do not cancel out but add, giving twice the angle compared with a single (forward) trip through the fibre (equation (5)). This is because the rotation direction of the nonlinear birefringence is different for the upper and lower hemisphere of the Poincar´e sphere (see figure 1(b)) contrary to birefringence in linear optics. Therefore, after reflection at the FM, which transforms the polarization state to its orthogonal counterpart (i.e. flipping it to the other hemisphere), the sense of rotation of the NPR during the return path will be the same as the forward path and the effects add up.
Figure 2.Experimental setup of the NPR measurement. DFB, distributed feedback laser; EDFA, erbium-doped fibre amplifier;
PC, polarization controller; FUT, fibre under test; FM, Faraday mirror; PBS, polarizing beam splitter.
3. Experiment 3.1. Setup
The experimental setup used to measure the NPR is shown in figure 2. The light source is a distributed feedback laser diode (DFB) operated in pulsed mode at a wavelength of 1559 nm, consecutively amplified by an EDFA (small signal gain 40 dB, saturated output power 23 dBm, where dBm is a physical unit of power). Typically, pulses with a duration of 30 ns, a repetition rate of 1 kHz and a peak power of up to 6 W were used. The light is then launched into the test fibre via a 90/10 coupler and a polarization controller. The coupler was inserted for the detection of the backward-travelling light after the double pass of the test fibre, with its 90-output port connected to the source in order to maintain the high launch powers into the test fibre. The polarization controller, PC1, allowed us to adjust the polarization of the light launched into the test fibre, which is important for the strength of the NPR as demonstrated by equation (5).
In order to satisfy the assumption of neglectable polarization mode coupling used in the previous section, a highly birefringent, PM fibre was used as the test fibre.
Its linear birefringence B is of the order of 5 ps m−1, corresponding to a beat length in the mm range. The fibre length was 200 m, giving a total of 400 m round-trip length of the light reflected by the FM.
The polarization state of the light after the double pass of the test fibre was examined by an analyser consisting of a polarization controller PC2 and a polarizing beam splitter (PBS). To achieve a good sensitivity of the analyser, it was calibrated to give a 50/50 output of the PBS for low-power signals where no nonlinear polarization rotation occurs.
Finally, the two PBS output channels were monitored by a fast photodiode (200 ps response time) and a sampling scope.
The measurements were then performed in the following way: for a given launch power, the polarization controller PC1 was adjusted to give the smallest possible output power at the monitored PBS channel. Consequently, the difference between the two PBS output channels is maximized, corresponding to a maximum value of the NPR.
316
Figure 3.Minimum output power of PBS channel 1 as a function of the launched power for a 200 m long PM fibre. Squares:
measured data; solid curve: prediction from our model; straight line: prediction in the absence of NPR. The deviations of the experimental data from the predicted values at high powers are due to modulation instability not included in the model.
Figure 4.Minimum output power of PBS channel 1 as a function of the launched power for a 100 m long PM fibre. Squares:
measured data; solid curve: prediction from our model; straight line: prediction in the absence of NPR.
3.2. Results
The experimental results are shown in figures 3 and 4.
In figure 3, the minimum output power (squares) of the monitored PBS channel is given as a function of the peak power in the test fibre. Note that the reported output power was normalized to account for the analyser losses and corrected for the PBS extinction ratio. Consequently, without any NPR, the reported output power would equal half of the power in the test fibre (straight line). As can be seen in figure 3, the effect of NPR is negligibly small up to about
In figure 3, the minimum output power (squares) of the monitored PBS channel is given as a function of the peak power in the test fibre. Note that the reported output power was normalized to account for the analyser losses and corrected for the PBS extinction ratio. Consequently, without any NPR, the reported output power would equal half of the power in the test fibre (straight line). As can be seen in figure 3, the effect of NPR is negligibly small up to about